High-precision magnetization intensity vector inversion method

Abstract

The invention relates to the field of magnetic vector inversion, in particular to a high-precision magnetization intensity vector inversion method, which comprises the following steps of: converting magnetic anomaly into normalized magnetic source intensity which is weakly sensitive to a magnetization direction; seamless partitioning based on data features is carried out according to the normalized magnetic source intensity data; and performing partition Gramian constraint on the three components of the magnetization intensity and the magnetization intensity obtained by NSS inversion to obtain a target function of magnetization intensity vector inversion based on data feature partition-normalized magnetic source intensity constraint, and performing magnetization intensity vector inversion by using the target function to obtain the magnetization intensity and magnetization direction distribution. In actual calculation, seamless partitioning is carried out based on normalized magnetic source intensity data characteristics for magnetic anomalies under complex residual magnetism conditions, physical property correlation constraint inversion is carried out on magnetization intensity three components of each sub-domain and a normalized magnetic source intensity data inversion result, and a high-precision magnetization intensity vector inversion result is obtained.

Description

Technical Field

[0001] The present invention relates to the field of magnetic vector inversion, and specifically to a high-precision magnetization intensity vector inversion method. Background Art

[0002] Magnetization intensity vector inversion takes into account the effects of remanent magnetization and demagnetization, and can directly obtain the underground magnetic structure and the distribution of magnetization directions. Currently, there are generally two common magnetization intensity vector inversion methods: one is to directly invert the three orthogonal components of the magnetization intensity vector (MMM); the other is to directly invert the magnetization intensity, inclination angle, and declination angle (MID).

[0003] The MID inversion method needs to estimate the magnetization direction before inversion and give an initial model. There are many magnetization direction estimation methods, but the conventional magnetization direction estimation methods are more suitable for simple isolated anomalies. The MMM inversion method can obtain reliable results without any prior information. However, compared with magnetic scalar inversion, the MMM inversion method needs to simultaneously invert the three components of the magnetization intensity, which increases the number of parameters to be solved and makes the inversion process unstable. Moreover, during the inversion process, the three components of the magnetization intensity (Mx, My, Mz) are independently modeled according to their own characteristics, and the obtained inversion results are often unrealistic. To address the above problems, currently, the Gramian constraint can be introduced during the magnetic vector inversion process, and the total magnetization intensity obtained by magnetic vector inversion is used to constrain the three components of the magnetization intensity, thereby obtaining stable results. This method is called the self-constrained inversion of the magnetization intensity vector. However, this method is not applicable to magnetic data under complex remanent magnetization conditions.

[0004] In actual situations, the underground conditions are very complex, and there are different magnetization directions in the same study area. Therefore, scholars divide the study area into sub-areas to make the inversion results more in line with the actual situation. For the magnetic vector inversion based on the Gramian constraint, scholars will divide the study area into sub-areas and then perform constrained inversion on each sub-domain to obtain more accurate magnetization intensity and magnetization direction. However, the sub-domains obtained by the current partitioning method cannot be pieced together, and the results are distorted in the non-coupling area. Summary of the Invention

[0005] Currently, the conventional magnetization intensity vector inversion method introduces the Gramian constraint during the inversion process of the three components of magnetization intensity. During the inversion, the three components of magnetization intensity are subjected to the Gramian constraint with the calculated total magnetization intensity to obtain a stable solution, which can also be called the self-constrained inversion of the magnetization intensity vector. However, for magnetic anomalies (different magnetization directions) under complex remanent magnetization conditions underground, the error of the three-component magnetization intensity vector inversion is relatively large, and the accurate distribution of the magnetization intensity vector cannot be obtained by using the self-result constraint. For the partitioned magnetic vector inversion based on the Gramian constraint, the study area is partitioned and the constrained inversion is performed on each subdomain to obtain a more accurate magnetization intensity and magnetization direction. However, the subdomains obtained by the current partitioning method cannot be pieced together, and the results are distorted in the uncoupled area.

[0006] The high-precision magnetization intensity vector inversion method based on data feature partitioning-normalized magnetic source intensity constraint proposed by the present invention can obtain the accurate underground magnetization intensity and magnetization direction distribution and improve the accuracy of the inversion result. The present invention provides the following technical solutions: A high-precision magnetization intensity vector inversion method includes the following steps: The first step is to convert the magnetic anomaly into a normalized magnetic source intensity that is weakly sensitive to the magnetization direction; The second step is to perform seamless partitioning based on data features according to the normalized magnetic source intensity data; The third step is to perform partitioned Gramian constraint on the three components of magnetization intensity and the magnetization intensity obtained by NSS inversion to obtain the objective function of the magnetization intensity vector inversion based on data feature partitioning-normalized magnetic source intensity constraint, and use the objective function of the magnetization intensity vector inversion based on data feature partitioning-normalized magnetic source intensity constraint to perform magnetization intensity vector inversion, and then the magnetization intensity and magnetization direction distribution can be obtained.

[0007] As a further solution of the present invention: the expression of the normalized magnetic source intensity is as follows: , C m = 10 - 7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source point and the observation point.

[0008] As a further solution of the present invention: performing seamless partitioning based on data features according to the normalized magnetic source intensity data includes the following steps: Search for the number of extreme points of the normalized magnetic source intensity data, which is the number of subdomains; Search around each extreme point as the center, and the amplitude less than half of the extreme point or the amplitude starting to increase is the initial boundary of the subdomain; Taking the initial area S of each subdomain and the distance R between the unpartitioned points and the extreme point of a certain subdomain as the reference for this subdomain, according to the ratio of the control area to the distance to allocate this point to the corresponding subdomain, and conduct the search again until the subdomain boundaries coincide, which is the subdomain boundary.

[0009] As a further solution of the present invention: The objective function of the magnetization intensity vector inversion under the data feature partition - normalized magnetic source intensity constraint is: , The kernel function matrix representing the three components of the magnetization intensity, is the three components of the magnetization intensity, represents the north component M x , the east component M y and the vertical component M z， is the magnetic anomaly data, is the kernel function matrix of the normalized magnetic source intensity, M N is the magnetization intensity obtained by inverting NSS, NSS is the normalized magnetic source intensity data, N is the number of sub - regions, W m is the model weighting function, is the dot product of vector groups, is the physical property vector within the i - th subdomain, is the regularization parameter, is the Gramian matrix parameter, is the calculated total magnetization intensity, is the three components of the magnetization intensity M M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix, is the partitioned Gramian matrix of the total magnetization intensity M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix.

[0010] Compared with the prior art, the beneficial effects of the present invention are: In actual calculations, for the magnetic anomalies under complex remanence conditions, the present invention conducts seamless partitioning based on the data characteristics of the normalized magnetic source intensity, and performs physical property correlation constraint inversion on the inversion results of the three components of the magnetization intensity and the normalized magnetic source intensity data in each subdomain to obtain high - precision magnetization intensity vector inversion results. This method improves the shortcomings of the existing methods. Through simulation experiments, it is verified that this method can improve the accuracy of the inversion results compared with the previous methods under complex remanence conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1It is a flowchart of the high-precision magnetization intensity vector inversion method in the embodiments of the present invention.

[0012] Figure 2 It is an example of magnetic anomaly and a partition effect diagram of two cubes in the embodiments of the present invention. Among them, (a) is a three-dimensional view and a magnetic anomaly map; (b) is a partition result based on data and a seamless partition result based on data characteristics.

[0013] Figure 3 It is an effect diagram of inverting the magnetic anomaly of two cubes in the embodiments of the present invention. Among them, (a) is the north component M of the self-constrained inversion result of the magnetic vector x ; (b) is the east component M of the self-constrained inversion result of the magnetic vector y ; (c) is the vertical component M of the self-constrained inversion result of the magnetic vector z ; (d) is the total magnetization intensity M of the self-constrained inversion result of the magnetic vector; (e) is the north component M of the magnetic vector inversion result of the algorithm of the present invention x ; (f) is the east component M of the magnetic vector inversion result of the algorithm of the present invention y ; (g) is the vertical component M of the magnetic vector inversion result of the algorithm of the present invention z ; (h) is the total magnetization intensity M of the magnetic vector inversion result of the algorithm of the present invention. Detailed implementation manners

[0014] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0015] 1. Self-constrained inversion of magnetization intensity vector:

[0016] The self-constrained inversion method of magnetization intensity vector is to add Gramian constraint to the inversion of magnetization intensity vector. Then, the objective function of the self-constrained inversion of magnetization intensity vector can be expressed as: . is magnetic anomaly data, are the three components of magnetization intensity, is the kernel function matrix of the three components of magnetization intensity, represents the north component M x , the east component M y and the vertical component M z， is the regularization parameter, W m is the model weighting matrix, is the calculated total magnetization intensity, is the Gramian matrix parameter, is the three components of magnetization intensity M M The Gramian matrix between the total magnetization M and each component is used to strengthen the linear correlation between the total magnetization to obtain a stable solution.

[0017] 2. Magnetization vector inversion based on normalized magnetic source intensity constraint: The expression of normalized magnetic source intensity is as follows: .

[0018] In the formula, C m =10 -7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source and the observation point. It can be seen that NSS is inversely proportional to the distance, proportional to the magnetic moment, has nothing to do with the magnetization direction, and has a good correspondence with the underground field source. The underground magnetic structure distribution can be obtained by inverting NSS. Therefore, the present invention constrains the three components of magnetization intensity by the normalized magnetic source intensity inversion result, so as to obtain reliable inversion results, and adds the Gramian matrix to the inversion objective function, so that the three components of magnetization intensity and the normalized magnetic source intensity inversion result are linearly correlated during the inversion iteration process. The objective function of magnetic vector inversion based on normalized magnetic source intensity constraint is as follows: .

[0019] In the formula, The kernel function matrix representing the three components of magnetization intensity, are the three components of magnetization intensity, Represents the north component M x 、East component M y and the vertical component M z， It is the magnetic anomaly data. is the kernel function matrix of the normalized magnetic source intensity, M N The magnetization intensity is obtained by inverting NSS, where NSS is the normalized magnetic source intensity data. m is the model weighting function, is the regularization parameter, is the Gramian matrix parameter, is the calculated total magnetization. is the three components of magnetization intensity M M and the magnetization M obtained by inverting NSS N The Gramian matrix of the enhanced magnetization intensity M M The magnetization M obtained by inverting NSS N The magnetization vector inversion is performed based on the linear correlation between them. is the total magnetization intensity M and the magnetization intensity M obtained by inverting NSS N of the Gramian matrix.

[0020] 3. Magnetization intensity vector inversion based on data feature partitioning - normalized magnetic source intensity constraint: In actual situations, magnetic bodies with different magnetization directions usually exist underground. Therefore, it is necessary to perform zonal inversion. To reduce the remanence interference, the present invention uses normalized magnetic source intensity data and proposes an adaptive seamless partitioning method according to the geometric characteristics of the normalized magnetic source intensity data. The partitioning steps are as follows: 1) Search for the number of extreme points of the normalized magnetic source intensity data, which is the number of subdomains.

[0021] 2) Search around each extreme point. The amplitude less than half of the extreme point or the amplitude starting to increase is the initial boundary of the subdomain.

[0022] 3) Take the initial area S of each subdomain and the distance R between the unpartitioned points and the extreme point of a certain subdomain as the reference for the subdomain. According to the ratio of the control area to the distance to assign this point to the corresponding subdomain and search again until the subdomain boundaries coincide, which is the subdomain boundary.

[0023] After the above - mentioned adaptive seamless partitioning, the study area is divided into N sub - regions with different magnetization directions. Then, physical property correlation constraint inversion is performed on the three components of the magnetization intensity of each subdomain and the magnetization intensity M obtained by inverting NSS N The objective function of the magnetization intensity vector inversion based on data feature partitioning - normalized magnetic source intensity constraint is as follows: .

[0024] In the formula, represents the kernel function matrix of the three components of the magnetization intensity, is the three components of the magnetization intensity, represents the north component M x , the east component M y and the vertical component M z， is the magnetic anomaly data, is the kernel function matrix of the normalized magnetic source intensity, M N is the magnetization intensity obtained by inverting NSS. NSS is the normalized magnetic source intensity data, N is the number of sub - regions, and W m is the model weighting function. is the dot product of vector groups, is the regularization parameter, is the Gramian matrix parameter, is the calculated total magnetization intensity, For the three components of magnetization intensity M M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix, is the total magnetization intensity M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix. Among them, is the physical property vector in the i-th subdomain and can be expressed as: .

[0025] Among them, i represents the number of the subdomain, and represents the physical properties of the whole area, represents the physical properties of the i-th subdomain.

[0026] Using the objective function of magnetization intensity vector inversion under the constraint of data feature partition-normalized magnetic source intensity can improve the accuracy of the inversion result and obtain the true underground magnetization intensity distribution and magnetization direction.

[0027] The following describes the specific implementation of the present invention in detail with specific embodiments.

[0028] Refer to Figures 1-3 , and calculate the magnetization intensity vector inversion of two underground cubes by the method of the present invention, Figure 2 (a) shows the cube distribution and magnetic anomaly results, Figure 2 (a) shows the three-dimensional positions and magnetic anomalies of two cubes with central positions at (900, 1000, -650) m and (2000, 1000, -800) m, and Table 1 shows the true physical parameters of the model.

[0029] Table 1 Physical parameters of the model

[0030] It can be seen from Table 1 that the magnetization intensities of the two cubes are 5 A / m, the dip angle and declination of the earth's magnetic field are I0 = 60°, D0 = 10°. The magnetization dip angle of cube 1 is I1 = -20°, the declination is D1 = 10°, the magnetization dip angle of cube 2 is I2 = 40°, and the declination is D2 = -20°. Figure 2 (b) shows the normalized magnetic source intensity and the results of two partitioning methods, Figure 2 The black frame in it represents the model position, the red circle defines the partitioning range based on the data, and the self-constrained inversion of the magnetization intensity vector is performed according to the partitioning result defined by the red circle. The white line divides the seamless partitioning range based on the data features, which is the partitioning result obtained by the partitioning method of the present invention. Comparing with the partitioning results of predecessors, the subregions obtained by the partitioning method of the present invention can process the entire region.

[0031] Figure 3 These are the inversion results of the method of the present invention and the self-constrained inversion method of magnetic vectors. Figure 3 The black frame in the figure represents the model position, and the black arrow represents the magnetization direction. Figure 3 (a)~ Figure 3 (c) shows the slice diagrams of the three-dimensional results of the M x , M y , M z components at y = 1000 m. Among them, the north component M x cannot show the position of cube 1, and the results diverge at cube 2, with a large deviation from the true value. The east component My and the vertical component Mz can reflect the positions of the two cubes, but they approach cube 2 at cube 1, and the results are distorted in the non-coupling region. For the total magnetization intensity M results obtained from the above three-component combination, see Figure 3 (d). The results diverge, and the true position of the model cannot be obtained, and its accuracy is 59.4%. Figure 3 (e)~ Figure 3 (h) shows the slice diagrams of the three-dimensional results of the M x , M y , M z components and the total magnetization intensity at y = 1000 m. Figure 3 The results show that the method of the present invention can accurately obtain the positions and boundaries of the two cubes, the obtained three-component data are closer to the true physical parameters of the model, and the inversion results are more convergent and smooth. The accuracy of the method of the present invention is 71.4%, and the present invention greatly improves the accuracy of the inversion results.

[0032] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A high-precision magnetization vector inversion method, characterized in that Including the following steps: First step, convert the magnetic anomaly into a normalized magnetic source intensity that is weakly sensitive to the magnetization direction; Second step, perform seamless partitioning based on data characteristics according to the normalized magnetic source intensity data; Third step, perform partition Gramian constraint on the three components of the magnetization intensity and the magnetization intensity obtained by NSS inversion to obtain the objective function of the magnetization intensity vector inversion under the partition-normalized magnetic source intensity constraint based on data characteristics. Use the objective function of the magnetization intensity vector inversion under the partition-normalized magnetic source intensity constraint based on data characteristics to perform magnetization intensity vector inversion, and the magnetization intensity and magnetization direction distribution can be obtained.

2. The high-precision magnetization intensity vector inversion method according to claim 1, wherein The expression of the normalized magnetic source strength is as follows: , C m = 10 -7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source point and the observation point.

3. The high-precision magnetization intensity vector inversion method according to claim 1, wherein The seamless partitioning based on data characteristics according to the normalized magnetic source intensity data includes the following steps: Search for the number of extreme points of the normalized magnetic source intensity data, which is the number of subdomains; Search around each extreme point as the center, and the amplitude less than half of the extreme point or the amplitude starts to increase is the initial boundary of the subdomain; Using the initial area S of each subdomain and the distance R from the unpartitioned point to the extreme point of a certain subdomain as the reference for that subdomain, according to the ratio of the control area to the distance to allocate this point to the corresponding subdomain, and conduct the search again until the subdomain boundaries coincide, which is the subdomain boundary.

4. The high-precision magnetization intensity vector inversion method according to claim 1 or 2 or 3, characterized in that The objective function of the magnetization intensity vector inversion under the partition-normalized magnetic source intensity constraint based on data characteristics is: ， The kernel function matrix representing the three components of magnetization intensity is the three components of magnetization intensity representing the north component M x , the east component M y and the vertical component M z， is the magnetic anomaly data is the kernel function matrix of the normalized magnetic source intensity, M N is the magnetization intensity obtained by inverting NSS. NSS is the normalized magnetic source intensity data, N is the number of sub-regions, W m is the model weighting function is the dot product of vector groups is the physical property vector within the i-th sub-region is the regularization parameter is the Gramian matrix parameter is the calculated total magnetization intensity is the three components of magnetization intensity M M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix is the partitioned Gramian matrix of the total magnetization intensity M and the magnetization intensity M obtained by inverting NSS N of the partitioned Gramian matrix

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